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Is a horse or a human more likely to have a pregnancy that lasts within 6 days of its mean

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Is a horse or a human more likely to have a pregnancy that lasts within 6 days of its mean


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Medical Science A medical research team has determined that for a group of 500 females, the length of pregnancy from conception to birth varies according to an approximately normal distribution with a mean of 266 days and a standard deviation of 16 days. (a) Use a graphing utility to graph the distribution. (b) Use a symbolic integration utility to approximate the probability that a pregnancy will last from 240 days to 280 days. (c) Use a symbolic integration utility to approximate the probability that a pregnancy will last more than 280 days.

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In this problem, we're told that if you add together the gestation period of an elephant, a rhino and a camel, you'll get 1520 days. And so, in this particular example, the gestation period of an elephant is represented by E of Orion. I was represented by our and of the camel is represented by sea. And so that's where you get the equation. If it's our policy, it was 1520.

And we're also told that if you take a camel stress station period and at 58 days to it, you get the gestation period of a rhino, which is where the second equation comes from. And then we're also told that if you take a camel's of gestation period, multiply attempts to and then subtract 162 days from that, you'll get the gestation period of an elephant, and that's where we get this through an equation. Now we're going to rewrite these equations to have all of the variables always on the left side of the equation and all of the constants always on the right side, and that way we can treat them as we would a normal system of equations. And so when we do this, we're going to treat E as X are as why and a C as Z. You can choose whichever one to assign to whatever normal variable were used to see.

In this case, I'm going to do with the way that I just said. And so when we subtract, are from both sides and subtracting 58th we get negative are plus C equal. When they get a 58 and then for the third equation, we're going to subtract it from both sides and add 162 to both sides. And when we do that, we'll see that negativity. Those two C is equal to 162 and now we're going to use the first equation the E specifically to eliminate the E and the third equation because we don't have any in the second equation.

And so when we do this, all we have to do is take the first equation and add it to the third equation to make the coefficient in front of the E and the third equation zero. And when we rewrite our equations, our first and second equations, they're going to stay the same and our third equation becomes E plus in ITV that zero e we get our plus zero r That's just are and we get C plus to see that's three C and then we get 15 20 plus 162. That is 1682. Okay, And now we're going to want to eliminate the are the third equation Now, normally, we would want a negative one right here as a coefficient for our and so what we're going to do as you can swap the second or third equations if you want to. However, it is also just simple to multiply the second equation times negative one make.

When we rewrite all of the equations, we get the same first equation. Okay, The second equation now becomes our minus C equals 58 and the third equation is our those three C is equal to 1682. Now, if you have noticed that if we just add added back here the second question to the third equation, you could have done that. However, I also think it's always good to make the coefficient if we're able to of the R and the second equation one. And so now we're going to take the second equation, multiply it times negative going and add it to the third equation in order to eliminate.

We are in the third equation, and when we do that, we get the same first equation, the same second equation as well. And the third equation becomes native R plus R, that zero r me a negative one times negative. See that see and into the three C and the third equation. We get four c. Make a note of one times 58 to 16 82.

We get 1000 600 in 24. Now we would divide both sides by a four. No, I just oversee. And when we do that, I will do the math out just so that you can see how it's done. You're more than welcome to use a calculator.

If you were allowed to do that. However, I also think it's good to just do the math, and so four was into 16 four times. That's 16. To track those you get zero. Bring down the to Ford is not going to to issue put a zero up here.

Then you get to bring down the four. Four goes into 24 6 times with no remainder, and so see is equal to 406. Now, we're going to plug that into the second equation in order to solve for our And so I'm going to use this equation right here. And I see the AR minus four or six tickle to 58. Add four or six to both sides will see the are this equal to 400 and a 64.

And of course, this isn't days and so see is equal to 406 days. That means the gestation period of camels for in our sixties R is equal to 464 days. And then now we want to solve for E. And to do that, we're going to plug the numbers we just found into the first equation. And we get e most 4 64 most 406 equal to 15 to 0 now 464 406 is 100 and 70.

So we have e possibly 8 70 because 15 20 If we subtract 8 70 from both sides, we get 650. And so we see that he this equal to 600 and 50 days, meaning that the gestation period of an elephant is 650 days and we have found our answers..

In exercise 15. We're considering a study of dummy fall syndrome. And here we are told that the average time between bath and onset of noticeable symptoms in a sample of six falls is 18.6 hours and the standard deviation is 1.7 hours. So already we've been given that the sample size n he is six. The sample mean He is 18.6 hours and the standard deviation S is 1.7 I was.

And we're also given that the time to answer of symptoms in all falls is normally distributed. So with that information we're going to be constructing and 90% confidence interval for the population. No, since the population standard division is not known and the sample size is small, the following formula will be applied expo plus Critical value 40 for the given level of significance, multiplied by the sample standard deviation where discourage opened and With a 90% confidence interval, The level of significant alpha is 1 -0.9, Which equals 0.1. When we have that, it's going to become 0.05. Next you want to get the degrees of freedom using N -1, which will be six minutes one and that equals five.

Now, the corresponding critical value of T for the 0.05 Level of significance and 5° of freedom equals 2.015. Now, with all that we have, we can substitute into the formula to get the 90% confidence interval. So it's going to be 18.6 class or minus 2.015 times 1.7 divided by the square root of six. This will be 18.6 plus or minus 1.40 when calculated, um, when tape that when we take that into the calculator, so this In ours is the 90% confidence interval for the mean time between bath and onset of no detectable symptoms..

Okay, we're gonna answer question number 27 in your textbook lengths of pregnancies, the lengths of pregnancies are normally distributed with a mean of 268 days in the standard deviation of 15 days. Uh So using the stop lit ap I chose normal distributions uh I mean 268 and a standard deviation of 15 pull out. The distribution Party says one class will use of. The normal distribution is inspired by a letter to Dear Abby and which your wife claimed to have given birth 308 days after a brief visit from her husband who was serving in the Navy. Given this information, find the probability of a pregnancy lasting 308 days or longer.

What does the results suggest? So the probability that the pregnancy last 308 days or longer, we want to the right of 308. I played the area and the probability is .38%. So what does this result suggest? Um well, it's very rare for pregnancy to last 308 days or more. So it's a it's a very rare occurrence. Um or it can also suggest that the husband is not the father, maybe she got pregnant um after he left.

Part B says if we stipulate that a baby is premature of the length of the pregnancy is in the lowest 3%. Find the length that separates premature babies from those who are not premature Premature babies often require special care. And this could result and helpful. This result could be helpful to hospital administrators in planning for that care. So we want to know what value corresponds to the lowest 3%.

So instead of calculating the area, we're going to calculate a value that corresponds to the bottom 3%, You want the area to the left a point of ray, And that's to 39.788. So we'll say approximately 240 days would be uh in the lowest 3% of all pregnancies..

In Probleble 54. The lens of preferences from conception to birth paris according to an approximately normal distribution. This normal distribution has a mean of 266 days. And the standard division of 16 days. We have said that it's approximately normal distribution for birthday.

We don't use a graphing utility to grab the distribution, distribution is normal. Then it has a function. One divided by sigma, blood by school route to buy deployed by eaters about minus x minus mu or square, divided by two sigma squid. We just enter sigma and mule in the graphing utility. Because I've entered dysfunction before.

That's refusing christmas. You put sigma equals 16 and new equals 206. 6 in the function here. Then when you grab the function, we have that here and this is the function. And we can increase the scale to make it -1 Point Home.

Two point. This is the distribution for barbie. We want to use an integration to approximate the probability that The pregnancy were lost from 240 days to 280 days. Then we want to get the probability for ex where X. Is the broken insolence to be between 240 And 208.

This This integration is from 240. for F of X. The X. F. Of X is defined in this most.

Then we need to enter the limits for this. Integration from equals 240 to be equals 200. And it's we can see that Approximately equals 4.75 steps. He says they Equals 0.757. We both see we will use this graphing utility or the integration utility To get the probability that Nancy will lost more than 200 and 80 days X.

To be more than 280 days equals the integration From 280 to Infinity. For f of X. Dx, there's a change of integration limits to make it From 280 two infinity infinity. We can just put very large number. We can see that It goes from 280 to infinity equals a point 191 4.19 What? And this is a final answer.

Marcy this for barbie and for body it's a graph..

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